Retrieving "Conserved Current" from the archives

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1. Symmetry Group

   Linked via "conserved currents"

   If a system's Lagrangian density $\mathcal{L}$ remains unchanged under a continuous set of transformations parameterized by a set of smooth angular variables $\theta^a$,
   $$\mathcal{L}(\phi, \partial\mu \phi) \to \mathcal{L}'(\phi', \partial\mu \phi') = \mathcal{L}(\phi, \partial_\mu \phi)$$
   then Noether's Theorem guarantees the existence of conserved currents $J^{\mu, a}$ associated with each generator of the symmetry:
   $$\partial_\mu J^{\mu, a} = 0$$